Array-Beamspace Mapping

We present a method for the recovery of two-dimensional angle-of-arrival information by beamspace processing using only a linear array of elements in the beam-forming processor. The method exploits the presence of grating lobes in beam patterns formed when using phased arrays with regularly spaced antenna elements. Periodic distribution of grating lobes in the reciprocal space allows, for some arrays, ‘unrolling’ a two-dimensional beamspace pattern into a linear distribution of beams, which is amenable to recovery using a linear array of elements in the beamspace processor. We develop mathematical underpinning of the approach and analyze several explicit examples of such array-beamspace (AB) mapping.